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Research Papers: Micro/Nanoscale Heat Transfer

# Modeling Carrier-Phonon Nonequilibrium Due to Pulsed Laser Interaction With Nanoscale Silicon Films

[+] Author and Article Information
Arvind Pattamatta

Department of Mechanical and Aerospace Engineering, University at Buffalo, Buffalo, NY 14260-4400apattamatta@gmail.com

Department of Mechanical and Aerospace Engineering, University at Buffalo, Buffalo, NY 14260-4400madnia@buffalo.edu

1

Corresponding author.

J. Heat Transfer 132(8), 082401 (Jun 04, 2010) (9 pages) doi:10.1115/1.4001101 History: Received April 08, 2009; Revised December 19, 2009; Published June 04, 2010; Online June 04, 2010

## Abstract

Ultrashort-pulsed laser irradiation on semiconductors creates a thermal nonequilibrium between carriers and phonons. Previous computational studies used the “two-temperature” model and its variants to model this nonequilibrium. However, when the laser pulse duration is smaller than the relaxation time of the carriers or phonons or when the carriers’ or phonons’ mean free path is larger than the material dimension, these macroscopic models fail to capture the physics accurately. In this article, the nonequilibrium between carriers and phonons in silicon films is modeled via numerical solution of the Boltzmann transport model (BTM), which is applicable over a wide range of length and time scales. The BTM is solved using the discontinuous Galerkin finite element method for spatial discretization and the three-stage Runge–Kutta temporal discretization. The BTM results are compared with previous computational studies on laser heating of macroscale silicon films. The model is then used to study laser heating of nanometer size silicon films, by varying parameters such as the laser fluence and pulse duration. From the laser pulse duration study, it is observed that the peak carrier number density, and maximum carrier and phonon temperatures are the highest for the shortest pulse duration of 0.05 ps and decreases with increasing pulse duration. From the laser fluence study, it is observed that for fluences equal to or higher than $1000 J/m2$, due to the Auger recombination, a second peak in carrier temperature is observed. The use of carrier-acoustic phonon coupling leads to equilibrium phonon temperatures, which are approximately 400 K higher than that of carrier-optical phonon-acoustic phonon coupling. Both the laser pulse duration and fluence are found to strongly affect the equilibrium time and temperature in Si films.

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## Figures

Figure 1

(a) Carrier temperature and number density profiles at the front surface of a Si film for L=2 μm, tp=75 fs, and ϕ=38.2 J/m2; (b) carrier and phonon temperature profiles at the front surface of a Si film for L=20 μm, tp=500 fs, and ϕ=1500 J/m2

Figure 2

Temporal variations in the (a) carrier number density, (b) carrier temperature, and (c) phonon temperature with pulse duration at the front surface for L=28 nm and ϕ=500 J/m2

Figure 3

Temporal variations in the (a) carrier number density, (b) carrier temperature, and (c) phonon temperature with laser fluence at the front surface for L=28 nm and tp=75 fs

Figure 4

Effect of carrier-phonon coupling on the temporal evolution of phonon temperature for L=28 nm and ϕ=3000 J/m2

Figure 5

Variations in the (a) equilibrium time and (b) equilibrium temperature with laser fluence for L=28 nm

Figure 6

Comparison of the BTM melting fluence threshold with the experiment

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